Virtu Financial and Optiver occupy a distinct tier within the quantitative finance landscape. They are not as frequently covered in prep guides as Jane Street or Citadel Securities, yet both firms are among the world's most sophisticated market-making operations, and both offer highly competitive careers for quantitative professionals.
What makes them distinct is their focus: Virtu is the paradigmatic technology-first market-maker, operating at scale across thousands of instruments globally; Optiver is the options specialist, with a 40-year track record in options market-making and a unique European cultural heritage. The interview styles at both firms reflect these differences, and knowing what each firm values before you walk in is a meaningful edge.
This guide covers both firms in depth: firm overviews, interview stages, representative question types, and actionable prep tips for each.
Part 01 · Virtu Financial
Virtu Financial overview
Virtu Financial was founded in 2008 by Vincent Viola and Douglas Cifu in New York City. Unlike many peer HFT firms, Virtu is publicly traded on NASDAQ (ticker: VIRT), which gives it an unusual level of public transparency for an industry known for opacity. In its 2015 S-1 filing, Virtu famously disclosed that it had been profitable on all but one trading day in a six-year span, crystallizing the public understanding of what technology-driven market-making can achieve.
Virtu operates as a global electronic market maker, providing liquidity across equities, fixed income, currencies, commodities, and derivatives in over 50 countries and across more than 235 trading venues. Its core competitive advantage is its execution and risk-management technology stack, not a strategy-first research shop, but an infrastructure-first trading operation.
Key facts: Virtu Financial
Roles at Virtu Financial
- Quantitative ResearcherPython, statistics, market microstructure, Strategy research, signal development
- Quantitative DeveloperC++, low-latency systems, Execution infrastructure, order management
- Algorithm DeveloperC++/Python, market data systems, Market-making algorithms
- Data ScientistPython, ML, data engineering, Analytics, quantitative research support
The Virtu interview process, stage by stage
Resume Screen
Quantitative academic backgrounds (math, CS, physics, financial engineering), systems programming experience, and market microstructure interest filter the initial pool.
Online Assessment (30-60 min)
Coding (Python/C++): data structures and numerical computing. Quantitative reasoning: probability and statistics. Basic market microstructure questions.
Technical Phone Screens (1-2 rounds)
45-60 min each: coding problem in Python or C++, two to three probability/statistics problems, resume deep-dive on quantitative projects, microstructure scenario questions.
Superday (3-5 Interviews)
Systems coding, probability and statistics, market microstructure depth, quant finance knowledge (options/risk), and fit interview.
Question types at Virtu Financial
Coding (Python/C++)
- Implement a rolling median in O(log n) using two heaps.
- Given a stream of price ticks, compute the VWAP over a sliding window with efficient updates.
- Parse a raw FIX protocol message and extract order fields.
- Design a rate-limiter for an API endpoint with specified throughput constraints.
Probability and statistics
- “You observe 100 coin flips, 60 of which are heads. Construct a 95% confidence interval for the bias parameter p.”
- “Given a geometric Brownian motion with μ = 0.08 and σ = 0.25, what is the expected log return over 1 year? What is the probability that the stock price exceeds 1.5× its current value in 2 years?”
- “What is the variance of the sum of n i.i.d. random variables with variance σ²? How does this change if the variables are correlated with coefficient ρ?”
Market microstructure
- “Explain adverse selection in the context of a market maker. How does a market maker protect itself?”
- “What is the Kyle lambda (price impact model) and how is it estimated from market data?”
- “A large institutional order hits your market. How do you update your quotes before and after the trade?”
Virtu-specific prep tips
- Study market microstructure seriously. Read Glosten-Milgrom, Avellaneda-Stoikov, and the intuition behind Almgren-Chriss. Understand adverse selection, inventory risk, and execution optimization at the level where you can reason about tradeoffs quantitatively.
- Python performance matters. Write code as if performance matters, use NumPy vectorized operations, avoid unnecessary loops, and show awareness of memory layout. Virtu interviewers notice candidates who write naturally efficient code.
- Be ready to discuss public Virtu data. Because Virtu is publicly traded, you can read their quarterly earnings calls, 10-K filings, and S-1. Know their capture rate trends, the KCG acquisition rationale, and payment for order flow dynamics.
Part 02 · Optiver
Optiver overview
Optiver was founded in 1986 in Amsterdam, making it one of the oldest active HFT and options market-making firms in the world. The firm began as a single trader on the Amsterdam Options Exchange and built into a global options market-making operation spanning equities, fixed income, ETFs, commodities, and foreign exchange.
Optiver is entirely employee-owned , no external investors, no PE backers, no public listing. The firm is known for its long-term perspective, its unusually strong Dutch-heritage culture (structured, collaborative, direct), and its genuine expertise in options market-making. The options focus distinguishes Optiver from Virtu: while Virtu trades across asset classes with a generalized model, Optiver has built deep specialization in volatility surface modeling and derivatives pricing.
Key facts: Optiver
Roles at Optiver
- TraderMental math, probability, options theory, Options market-making, volatility trading
- Quantitative ResearcherStatistics, ML, Python/C++, Signal research, model development
- Software DeveloperC++, distributed systems, Trading infrastructure
- Risk ManagerDerivatives risk, statistics, Position risk management
The Optiver interview process, stage by stage
Application and Sourcing
Campus programs at Amsterdam, Delft, ETH, MIT, U Chicago, CMU, Imperial. Strong pipeline from math olympiad and competitive programming backgrounds.
The '80 in 8' Mental Math Test
80 arithmetic problems in 8 minutes without a calculator. ~40-50% of candidates fail to meet Optiver's threshold. This is a hard filter, not a courtesy screen.
Numerical Reasoning + Personality Assessments
SHL-style numerical reasoning (harder than standard) plus a situational judgment or personality inventory.
Video/Phone Interview (30-45 min)
Live mental math, two to three probability problems, options/trading concepts for the Trader track, and cultural fit discussion.
Superday (Amsterdam, Chicago, or Sydney)
Advanced probability, options theory (Trader track), live mental math round, market-making simulation, coding assessment, and final HR interview.
Question types at Optiver
Mental arithmetic, the 80 in 8 format
Optiver's mental math emphasis is the highest of any major HFT firm. 6 seconds per problem maximum. Expect:
- “What is 47 × 83?”(Answer: 3,901, compute in under 8 seconds.)
- “What is 144 ÷ 16? What is 7/9 as a percentage to two decimal places?”(Fractions and division under time pressure.)
- “A stock moves from $84 to $91. What is the percentage gain?”(Compound computation: (91-84)/84 × 100.)
Probability and statistics
“You flip a fair coin until you get two heads in a row. What is the expected number of flips?”
“Cards are drawn from a shuffled 52-card deck. You can stop at any time and win $1 if the next card is red. What is the optimal stopping strategy?”
“A drunk takes steps of ±1 with equal probability starting at 0. What is the expected number of steps to reach +3?”
Options theory (trader track)
- “Walk me through the derivation of put-call parity. What are the assumptions required?”
- “If a stock moves up $1, what happens to the value of an at-the-money call? An in-the-money call? Explain in terms of delta.”
- “Why does implied volatility vary across strikes (the vol smile)? What does this tell you about the market's implied distribution?”
- “You are quoting a delta-neutral straddle. Overnight, realized volatility picks up significantly. What happens to your P&L? Why?”
Market-making simulation (legendary)
Optiver's market-making game is legendary among HFT interview candidates. Common formats:
- The Dice Game. Interviewer rolls a concealed die; candidates make markets and update quotes as partial information arrives (e.g., 'the result is even').
- The Jar Game. A jar contains an unknown number of marbles; candidates sample and market-make the count, narrowing spreads as more samples arrive.
- Stock Simulation. Multi-round competitive trading where candidates quote bid-ask spreads, manage inventory, and update prices based on trade flow.
Evaluation criteria: rational quote updates, controlled inventory, disciplined spread management, and verbalizing the reasoning behind every price change.
Optiver-specific prep tips
- The '80 in 8' is pass/fail, treat it first. Before any other prep, time yourself with a strict 8-minute clock on 80 mixed arithmetic problems. If your pass rate is below 80%, address that before anything else.
- Study options theory with real market context. Optiver's options questions are not purely textbook. Study skew, term structure, and the relationship between realized and implied volatility. Hull's Options, Futures, and Other Derivatives is a good foundation; Taleb's Dynamic Hedging provides the practitioner intuition.
- Practice verbalizing market-making logic. The most common failure mode is silent updating, candidates change their quotes but do not explain why. Practice with a partner: have them give you information incrementally and narrate every quote adjustment.
- Understand Optiver's cultural values. Optiver has a distinctive Dutch-rooted culture: direct communication, intellectual honesty, and genuine interest in markets. They look for candidates excited about options market-making, not just chasing compensation.
Section · Preparation
Your preparation plans
For Virtu Financial, 8-week plan
Market microstructure foundations
Adverse selection, Kyle lambda, order book dynamics, Glosten-Milgrom, Avellaneda-Stoikov.
Coding: Python performance + C++ algorithmic prep
LeetCode medium/hard, NumPy vectorization, data structure problems, performance-aware Python.
Probability and financial statistics
Stochastic processes basics, Shreve Vol I, GBM intuition, confidence intervals, hypothesis testing.
Virtu-specific research
Read earnings calls, 10-K filings, KCG acquisition rationale, payment for order flow dynamics.
Mock technical interviews
Full mock superdays across coding, probability, and microstructure.
For Optiver, 10-week plan
Mental arithmetic drilling
20-30 min/day minimum, every day. Timed arithmetic: multiplication, fractions, percentages. Build to 80/8 min reliably.
Probability: expected value, conditional probability, stopping times
Zhou Green Book, Mosteller Fifty Challenging Problems, random walk recurrences, Markov chains.
Options theory: Greeks, put-call parity, vol surfaces
Hull chapters 17-21, straddles/strangles/straddle P&L, implied vs realized vol, skew intuition.
Market-making simulation practice with a partner
Optiver-style dice and jar games, narrate every quote adjustment, manage inventory consciously.
Full mock superday + weak-area drilling
End-to-end practice, timed arithmetic review, options theory rapid-fire questions.
Key takeaways
Virtu and Optiver are two of the most technically demanding employers in quantitative finance, and two of the most rewarding for candidates who match their respective profiles.
Virtu rewards systems thinking
Candidates who understand market infrastructure, write performant code, and can reason about scaling a market-making model across thousands of instruments stand out.
Optiver rewards options specialization
Internalize the math and market dynamics of derivatives. Be precise under pressure and verbalize the probabilistic reasoning behind every quote.
The '80 in 8' arithmetic test is non-negotiable for Optiver
Drill arithmetic for 20+ min/day starting at least four weeks out. Candidates who skip this preparation typically fail the filter regardless of theoretical skill.